Amplifiers are systems that increase the power of a signal. An electronic amplifier takes power from a power supply and shapes its output to match the input signal. The first electronic amplifiers were used in communication systems. One of the earliest examples of such a circuit is the Audion described in U.S. Pat. No. 841,386 to De Forest. Today, amplifiers are an indispensible portion of nearly all analog and mixed-signal electronic systems. Amplifiers have myriad uses including increasing the power of a communication signal for transmission through a wireless network, adjusting the strength of an audio signal to a desired volume, and making a sensor signal more readily convertible to a digital format.
In electronic circuit design, a differential architecture is one in which the carried signal is defined by the difference in potential between two nodes that have equal and opposite excursions from a fixed potential. The fixed potential voltage is called the common mode voltage. For example, two children on a rigid see-saw are at any moment an equal and opposite distance from the fulcrum of the see-saw. When they are even with the fulcrum, the differential signal they represent is zero. When the children are at a maximum distance from the fulcrum they are an equal distance away in opposite directions, and the differential signal they represent is at a maximum. A differential architecture can be contrasted with a typical single-ended circuit wherein the signal is defined by the difference in voltage between a single signal node and a fixed potential. Using the same example, at any moment the distance from a single child's center of gravity to the ground represents a single-ended signal.
In today's high-performance analog and mixed-signal circuits, the dominant architecture for amplifier circuits is differential. The first differential amplifier was described in U.K. Pat. No. 482,470 to Blumlein. Differential architectures are favored because they are inherently resistant to noise. As described above, a differential signal is defined as the difference between the potentials on two nodes. Since both nodes are likely affected by noise to the same degree, the operation of subtracting the voltage on one node from the voltage on the other will effectively subtract out the noise from the signals. Returning to the see-saw example, noise in the circuit could be analogized to an earthquake striking the park where the see-saw was located. The difference between the positions of the two children would be unaffected by the rolling of the earth because each would be rising and falling with the fulcrum in tandem. However, the height of a single child would be disturbed from the norm because the fulcrum of the see-saw and the ground directly beneath the child could be at different elevations due to the wave-like movement of the ground during the earthquake.
There are numerous variations between a real world amplifier and its ideal. These variations have been studied and categorized extensively over the past century. Three key aspects of a differential amplifier's performance that vary from the ideal are the amplifier's output swing, common mode rejection ratio (CMRR), and gain. The gain of an amplifier is the factor by which the power of the input signal is increased by the amplifier. This value should remain constant despite the varying common mode level of the input signal and other variations in the amplifier's operating conditions. For a differential amplifier, the gain value is usually represented by the symbol ADM. The output swing of the amplifier is the span of voltages or currents the amplifier is able to produce at its output without degrading the signal. The CMRR of an amplifier is a measure of how well the amplifier ignores the common mode voltage of the input signal while amplifying the difference between the two components of the input signal.
Description of an amplifier's CMRR requires that a distinction be made between differential gain ADM, and common mode gain ACM. An ideal differential amplifier will produce an output signal that is completely free of the influence of that portion of the input signals which is common to both of the input signals. No amplifier is completely ideal, so each will produce an output signal that is equivalent to the common mode of the input signal multiplied by the common mode gain of the amplifier. An ideal differential amplifier that outputs a single-ended signal has a common mode gain of zero. The CMRR of a differential amplifier is proportional to the logarithm of ADM divided by ACM. Since undesired common mode gain will result in a portion of the output signal being erroneous, and the overall size of the output signal is set by the differential gain, the CMRR is a representation of the degree to which the common mode gain corrupts the output signal. An ideal differential amplifier that outputs a single-ended signal will have a CMRR of infinity.
The circuit illustrated in FIG. 1 belongs to a class of differential amplifiers known as instrumentation amplifiers. This particular configuration uses three operational amplifiers, and has been used and studied extensively in the prior art. The instrumentation amplifier in FIG. 1 takes in the components of a differential signal on the nodes V− and V+. The illustrated circuit is a single-ended differential amplifier because the amplified output signal is provided in single-ended format on node VOUT. The circuit is commonly used in measurement and test equipment because it has extremely high input impedance. In other words, amplifier 101 and amplifier 102 draw extremely low currents from nodes V− and V+ respectively which allows the circuit to sample very delicate signals without disturbing them. The circuit also has high gain as discussed below.
The gain of the instrumentation amplifier in FIG. 1 is best understood by analyzing the circuit in two stages. The first stage of the amplifier is comprised of amplifier 101, amplifier 102, and resistors 103, 104, and 105. In an ideal circuit, resistor 104 and 105 are equivalent. Without resistor 103, the remaining components would act as unity-gain buffers. However, with the addition of resistor 103, the gain of the input stage increases considerably. The ideal differential gain of the first stage is:ADM1=1+(2×R104)/R103 In the previous equation, ADM1 is the differential gain of the first stage, and the R values are the resistance values of resistors 103, and 104 as indicated by their subscripts. The second stage of the amplifier in FIG. 1 is comprised of amplifier 106, and resistors 107, 108, 109 and 110. Resistors 107 and 108 are equivalent in an ideal circuit. Resistors 109 and 110 are also equivalent in an ideal circuit. The ideal differential gain of the second stage is:ADM2=−R109/R107 In the previous equation, ADM2 is the differential gain of the second stage, and the R values are the resistance values of resistors 109, and 107 as indicated by their subscripts. The overall gain of the amplifier is the product of the gains of the individual stages. This overall gain value describes the ratio of the differential signal at the input of the amplifier to the single-ended signal at the output of the amplifier.
The CMRR of the circuit in FIG. 1 has been studied extensively because rejection of common mode noise is one of the key advantages of this circuit. If all of the resistors and amplifiers in FIG. 1 are ideal, the common mode gain of the circuit is zero. In this case, the single-ended output voltage is precisely equal to the difference between the input voltages multiplied by the differential gain derived above. However, if the resistors do not match, or the CMRRs of amplifiers 101, 102, and 106 are less than infinity, the common mode gain of the circuit will be greater than zero, and the CMRR of the circuit will not be infinite.
Typical amplifiers used for amplifiers 101, 102, and 106 have extremely high CMRRs in the range of 130 to 140 decibels (dB) thereby allowing a simplified analysis which considers the amplifiers to be ideal. As such, the first stage in its entirety will have very little effect on the CMRR of the overall circuit. However, the same cannot be said for the resistors in the second stage. If resistor 109 does not match resistor 110, or if resistor 107 does not match resistor 108, the CMRR of the circuit can be seriously affected. With the above mentioned simplification for ideal amplifiers, the common mode gain of the circuit in FIG. 1 can be expressed as:ACM=[(R109+R107)×R110−(R110−R108)×R109]/[(R110+R108)×R107]In the previous equation, ACM is the common mode gain of the system, and the R values are the resistance values of resistors 107, 108, 109, and 110 as indicated by their subscripts. If the pertinent resistors in the above equation are perfectly matched, the common mode gain of the circuit would drop to zero.
The common mode gain equation above for the circuit in FIG. 1 can be used to test the sensitivity of the CMRR of the circuit to variations in resistor values. In a circuit where resistor 109 and resistor 110 are designed to be 100 kilohms (kΩ), and resistor 108 and 107 are designed to be 1 kΩ, but resistor 109 is larger by 1%, the ACM of the circuit would be roughly 0.01. In this case, the output signal would have roughly 20 millivolts (mV) of common mode output voltage for every 2 volts (V) of common mode input. It is for this reason that real world applications of this circuit require either highly accurate resistors, or adjustable resistors that are trimmed once the circuit is fabricated. Although this can improve the CMRR of the circuit, both approaches are very expensive. Therefore, the CMRR of the circuit in FIG. 1 is the cause of some concern.
The output swing of the circuit in FIG. 1 is also problematic. Implementations of the circuit in FIG. 1 often use what is called a rail-to-rail amplifier for amplifier 106. These designs suffer from the fact that rail-to-rail amplifiers are generally unable to truly swing from the supply rail to the ground rail. The output of these amplifiers might not be able to swing down below 25 mV. As a result, a portion of the information contained in the input signal is lost as the amplifier “clips” off what should ideally be an output signal below the minimum output voltage of amplifier 106.